Synchronization in dynamical networks with unconstrained structure switching

Abstract

We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly, from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows to extend the Master Stability Function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the the dynamics of the units.

8 pages, 3 figures. arXiv admin note: text overlap with arXiv:1407.0742

References in corpus (4)

• The structure and dynamics of multilayer networks
• Enhancing complex-network synchronization
• Synchronization in scale-free network with asymmetric coupling
• Temporal networks: slowing down diffusion by long lasting interactions

Cited by in corpus (6)

• The synchronized dynamics of time-varying networks
• Synchronization in networks with multiple interaction layers
• Finding network communities using modularity density
• Influence of cumulative damage on synchronization of Kuramoto oscillators on networks
• Effects of time-varying habitat connectivity on metacommunity persistence
• Theory of synchronisation and pattern formation on time varying networks